About this model
An ideal line vortex is a fundamental model in fluid dynamics representing a two-dimensional, incompressible, and irrotational flow field with a singular point at its center. The flow is purely azimuthal, meaning fluid particles move in concentric circles around the vortex axis. The tangential velocity, v_θ, is given by the equation v_θ = Γ/(2πr), where Γ (Gamma) is the constant circulation around any closed loop enclosing the vortex center, and r is the radial distance from the center. This velocity profile shows that speed is inversely proportional to radius, creating a singularity (infinite velocity) at r=0. The flow is irrotational (∇ × v = 0) everywhere except at the singular line itself, where vorticity is concentrated. This model is a key example of potential flow, derived from a velocity potential φ = (Γθ)/(2π), and its streamlines are circles. By interacting with this simulator, students can visualize the non-intuitive relationship between velocity and radius, explore the concept of circulation as a global property of the flow, and understand how a flow can be irrotational yet still possess a net rotation. The model simplifies real vortices by neglecting viscosity, three-dimensional effects, and core structure, focusing purely on the kinematic consequences of a concentrated vorticity distribution.
Who it's for: Undergraduate students in fluid dynamics or aerodynamics courses studying potential flow theory and vortex dynamics.
Key terms
- Ideal Vortex
- Circulation
- Potential Flow
- Irrotational Flow
- Velocity Field
- Singularity
- Stream Function
- Azimuthal Velocity
Frequently asked questions
- If the fluid is swirling in circles, how can the flow be called 'irrotational'?
- In fluid dynamics, 'irrotational' means the local fluid elements do not spin about their own axes (their vorticity is zero). In an ideal line vortex, while the fluid moves in circular paths, each infinitesimal element translates and deforms without net rotation. The 'rotation' we see is a global, orbital motion, not local spinning. This is a key distinction between a vortex and a rotating rigid body.
- What does the circulation Γ physically represent, and is it conserved?
- Why does the velocity become infinite at the center (r=0), and is this realistic?
- Where do we see approximations of ideal vortex flow in the real world?